[{"key":"dc.contributor.author","value":"Bergeron, Maxime Octave","language":null},{"key":"dc.date.accessioned","value":"2016-08-10T16:28:04Z","language":null},{"key":"dc.date.available","value":"2016-08-11T02:01:57","language":null},{"key":"dc.date.issued","value":"2016","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/58741","language":null},{"key":"dc.description.abstract","value":"The goal of this thesis is to understand the topology of representation varieties. To be more precise, let G be a complex reductive linear algebraic group and let K \u2282 G be a maximal compact subgroup. Given a finitely generated nilpotent group \u0393, we consider the representation spaces Hom(\u0393,G) and Hom(\u0393,K) endowed with the compact-open topology. Our main result shows that there is a strong deformation retraction of Hom(\u0393,G) onto Hom(\u0393,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(\u0393,G)\/\/G onto the ordinary quotient Hom(\u0393,K)\/K. Using these deformations, we then describe the topology of these spaces.","language":"en"},{"key":"dc.language.iso","value":"eng","language":"en"},{"key":"dc.publisher","value":"University of British Columbia","language":"en"},{"key":"dc.rights","value":"Attribution-NonCommercial-NoDerivatives 4.0 International","language":"*"},{"key":"dc.rights.uri","value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","language":"*"},{"key":"dc.title","value":"The topology of representation varieties","language":"en"},{"key":"dc.type","value":"Text","language":"en"},{"key":"dc.degree.name","value":"Doctor of Philosophy - PhD","language":"en"},{"key":"dc.degree.discipline","value":"Mathematics","language":"en"},{"key":"dc.degree.grantor","value":"University of British Columbia","language":"en"},{"key":"dc.date.graduation","value":"2016-09","language":"en"},{"key":"dc.type.text","value":"Thesis\/Dissertation","language":"en"},{"key":"dc.description.affiliation","value":"Science, Faculty of","language":"en"},{"key":"dc.description.affiliation","value":"Mathematics, Department of","language":"en"},{"key":"dc.degree.campus","value":"UBCV","language":"en"},{"key":"dc.description.scholarlevel","value":"Graduate","language":"en"},{"key":"atmire.cua.enabled","value":"","language":""}]